Mechanical Properties of Fluids

Two liquids A and B have A and B as contact angles in a capillary tube. If K = A / B, then identify the correct statement:

1. K is negative, then liquid A and liquid B have convex meniscus.
2. K is negative, then liquid A and liquid B have concave meniscus.
3. K is zero, then liquid A has convex meniscus and liquid B has concave meniscus.
4. K is negative, then liquid A has concave meniscus and liquid B has convex meniscus.

Consider a completely full cylindrical water tank of height 1.6 m and of cross-sectional area 0.5 m2. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is: (g = 10 m/s2)

1. 2 m/s
2. 5 m/s
3. 3 m/s
4. 4 m/s

A solid steel ball of diameter 3.6 mm acquired terminal velocity 2.45 10-2 m/s while falling under gravity through an oil of density 925 kg m-3. Take density of steel as 7825 kg m-3 and g as 9.8 m/s2. The viscosity of the oil in SI unit is

1. 2.18
2. 1.68
3. 2.38
4. 1.99

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is n times the volume of the bubble B, then, the value of n is .

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 cm2 with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density 1.5 103 kg/m3. What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity = 10 m/s2)

Two water drops each of radius 'r' coalesce to form a bigger drop. If 'T' is the surface tension, the surface energy released in this process is :

1. 4 r2 T [2 - 21/3 ]
2. 4 r2 T[1 + 2]
3. 4 r2 T [2 - 22/3 ]
4. 4 r2 T[ 2 - 1]

In a hydraulic lift, the surface area of the input piston is 6 cm2 and that of the output piston is 1500 cm2. If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is kJ.

Consider following statements: Choose the correct answer from the options given below:

1. B, C, D Only
2. C, D, E Only
3. A, D, E Only
4. A, B, C Only

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water? (Given: density of water = 1000 kg m-3)

1. 400 cm3
2. 600 cm3
3. 1400 cm3
4. 4000 cm3

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/m3. If the pressure inside the bubble is 2100 N/m2 greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g=10 m/s2)

1. 0.02
2. 0.05
3. 0.25
4. 0.1